Comparative quantum-classical dynamics of natural and synthetic molecular rotors show how vibrational synchronization modulates the photoisomerization quantum efficiency

We use quantum-classical trajectories to investigate the origin of the different photoisomerization quantum efficiency observed in the dim-light visual pigment Rhodopsin and in the light-driven biomimetic molecular rotor para-methoxy N-methyl indanylidene-pyrrolinium (MeO-NAIP) in methanol. Our results reveal that effective light-energy conversion requires, in general, an auxiliary molecular vibration (called promoter) that does not correspond to the rotary motion but synchronizes with it at specific times. They also reveal that Nature has designed Rhodopsin to exploit two mechanisms working in a vibrationally coherent regime. The first uses a wag promoter to ensure that ca. 75% of the absorbed photons lead to unidirectional rotations. The second mechanism ensures that the same process is fast enough to avoid directional randomization. It is found that MeO-NAIP in methanol is incapable of exploiting the above mechanisms resulting into a 50% quantum efficiency loss. However, when the solvent is removed, MeO-NAIP rotation is predicted to synchronize with a ring-inversion promoter leading to a 30% increase in quantum efficiency and, therefore, biomimetic behavior.

optimized geometry reproducing the wavelength of the corresponding absorption maxima (λmax).
Where 200 snapshots (geometries and velocities) were extracted during the dynamics at 100 ps time intervals after a suitable equilibration time, starting from these snapshots, 200 HF/6-31G*/Amber were propagated for 200 fs and then followed by corresponding S0 2-root-stateaverage CASSCF/6-31G*/Amber for 50 fs.The 200 geometries and velocities of the final snapshot of the 50 fs propagation are assumed to represent the Boltzmann distribution (to best account for the PES anharmonicity, a Boltzmann or Wigner sampling based on the Hessian Matrix were not considered) and, therefore, the initial conditions for subsequent quantum-classical trajectory computations starting on S1.All calculations were performed using Molcas/Tinker package. 5,6O-NAIP@MeOH QMMM model, population dynamics, and initial conditions.The model of MeO-NAIP@MeOH was constructed via classic molecular dynamics equilibration with periodic boundary conditions (Fig S1b).The MeO-NAIP molecule was taken from a previously reported work 7 (as described in ref. 7; this corresponds to the Z diastereoisomer.Therefore, the investigated isomerization process is Z to E. The E to Z process is not investigated here also due to the lack of corresponding experimental studies).The optimized chromophore is then embedded in the center of a cubic box of size 60 x 60 x 60 Å, containing methanol (MeOH) solvent molecules.
The chromophore is kept frozen, and the solvent system is minimized at the molecular mechanics (MM) level, using the conjugate-gradient method with periodic boundary conditions.The nuclear charges of the chromophore atoms for this purpose are calculated using the Electrostatic Potential Fitting Method (ESPF) at the MP2/6-31G* level.The binding and van der Waals parameters are taken from the OPLS_aa force field 8 .The minimized chromophore-solvent system is then relaxed using a 5 ns long molecular dynamics (MD) simulation under the isothermal-isobaric ensemble (NPT), set at 1 atm of pressure and 298 K of temperature using the GROMACS software package 9 .During the first 0.3 ns of the simulation, the system gradually thermalizes to 298 K, equilibrates for the next 0.7 ns, and relaxes for the next 4 ns.From this dynamic simulation step, named production, snapshots are extracted every 10 ps, involving a 20-Å solvent layer to complete a full set of 400 configurations to define the hybrid quantum mechanics / molecular mechanics (QM/MM) model.In this model, the chromophore is treated at the QM level using the complete active space self-consistent field (CASSCF) method with a 6-31G* basis set and an active space comprising 12 electrons in 11 orbitals (CASSCF/631-G*/ 12,11).The solvent molecules, located at 4 Å from any chromophore atom, are treated at the MM level (OPLS_aa force field) and are allowed to move during the QM/MM molecular dynamics while the rest of the solvent group remains frozen.The QM/MM dynamics are computed following a single-root CASSCF gradient for 200 fs with a time step of 1 fs (41.3 au), and geometries and velocities of the final snapshot are assumed to represent the Boltzmann distribution (to best account for the PES anharmonicity, a Boltzmann or Wigner sampling based on the Hessian Matrix were not considered) and, therefore, the initial conditions for subsequent quantum-classical trajectory computations starting on S1.All calculations were performed using Molcas/Tinker package. 5,6PSB11 and MeO-NAIP isolated model generation.In order to study the protein and survey the induced environmental effects, we repeat the above initial condition calculations for the two isolated chromophores (i.e. in the absence of the protein and methanol solvent for Rh and MeO-NAIP respectively).Therefore, the sampling is limited to the isolated retinal chromophore with a terminal -C15=N-CεH3 group and to the MeO-NAIP cation, corresponding to the same structure employed during solvated study described above, but now in isolated conditions.Therefore, the protocol followed for the initial conditions generations was the same described in the section above but the lack of the environment: protein or methanol, according to each model removes the MM side (protein or solvent atoms treated at MM level) from the previously described QMMM model.In this isolated model, the chromophore is still treated at the QM level using the complete active space self-consistent field (CASSCF) method with a 6-31G* basis set and the corresponding previously reported active space CASSCF/6-31G*.Notice that the MeO-NAIP switch is not a chiral molecule, which means it will create a combination of enantiomers resulting in both clockwise and counterclockwise isomerization, yielding equal statistics.
Final comments on computational methodology.The employed 2-root-state-average CASSCF for Rhodopsin and a 3-root-state-average CASSCF for MeO-NAIP are given for the following reasons: i) These levels reproduce measured dynamics and utilize single-point CASPT2 corrections for measured spectroscopic observables.ii) In the case of Rhodopsin, the introduction of the S2 in the CASSCF (i.e.S0, S1, and S2 state averaging) calculation makes the S1 potential energy surface too flat, generating too long excited state lifetimes.The interaction of the S1 and S2 states when the retinal is modeled inside the protein environment has been proven to be very limited, demonstrating that S2 inclusion does not significantly impact the dynamics 10 .iii) In the case of MeO-NAIP, a strategy based on S0, S1, and S2 state averaging had to be applied instead.
The reason for this change is that the synthetic system has much higher excitation energies (it absorbs UV-light rather than visible-light) and features a much smaller S2-S1 energy gap.In fact, in contrast to Rhodopsin, most of the initial conditions selected to initiate quantum-classical trajectory calculations, at the CASSCF level, show S2 being the spectroscopic state, and it was therefore necessary to start the trajectory from S2 rather than S1.This approach aligns with the protocol benchmarked and adopted in references 11,12 .In essence, we believe a model that captures experimental observables enhances our ability to elucidate reaction mechanisms.

Section II. Excited state lifetime.
The excited-state quantum-classical trajectories were propagated at the 2-root-state-average CASSCF/6-31G*/Amber and 3-root-state-average CASSCF/6-31G*/OPLS-aa level for Rh and MeO-NAIP respectively, following the Tully surface-hop method including the decoherence correction 13,14 .(A test supporting the validity of the Tully surface-hopping method for alkylated or protonated Schiff bases has been recently reported. 15) The state average was determined according to the values of the oscillator strength presented for each system.All calculations were performed using Molcas/Tinker package. 5,6In order to determine the S1 lifetime reported in Table 1, we have used three different approaches: i) following fitting formula (1) comprising a lag time and two exponential decay time, ii) the time what the system decay to half of the S1 population decay, and iii) average of decay time.
The rPSB11@Rh model has been previously validated and consequently referenced in the Table S1 below.This section will focus on the MeO-NAIP@MeOH model, and the validation carried out by predicting the values of a set of properties relevant to the photophysical and photochemical behavior of these systems, which are then compared to the available experimental values.These properties following a comparative aim with the already validated rPSB11@Rh model are: 1) λmax value and corresponding absorption band.
4) Excited state vibrational frequencies for δop and BLA.
.h.Observed data from ref. 21 .i. Observed data from ref. 7 .j. Observed data from ref. 22 We evaluated the λmax value (property 1) from the absorption band (Fig. S2a) computed at the 3root-state-average CASPT2//CASSCF/6-31G*/ OPLS_aa level of theory.As reported in Supplementary Table S1, the computed 383 nm value is in close agreement with the observed value of 389 nm.The results of the population dynamics allowed us to predict the rest of the properties analyzed.To compute the "photoproduct appearance time," (property 2) we use both excitation energy as well as geometrical criteria.For the excitation energy, we selected the small group of trajectories reaching the faster ISS1/S0 and leading to successful decay events.We define the shortest time employed by the fastest trajectory to match the computed e-isomer photoproduct absorption λmax value as the upper limit to the photoproduct appearance time (Fig. S2b).The trajectory matches the photoproduct absorption value at 348 fs, considering this time as a predicted photoproduct appearance time, which may be compared with the experimental results suggesting photoproduct detection at time scales higher than 300 fs.The e-isomer photoproduct equilibrium structure necessary for the computation of the photoproduct appearance time defined above was generated by performing an S0 geometry optimization at the CASSCF/6-31G*/OPLS_aa level from one snapshot (geometry) of the trajectories analyzed once the molecule hop and relaxed on S0 potential surface.The equilibrium e-isomer structure whose λmax value was determined via a vertical excitation energy calculation at the 3-root-state-average CASPT2//CASSCF/6-31G*/OPLS_aa level presenting a value of 304 nm (94 kcal mol -1 ).The excited state lifetime (property 3) is computed by following different approaches yielding equivalent results: i) fitting the S1 population decay with a previously employed Gaussian-plus-exponential equation ( 1) 16 (Fig. S2c), ii) taking the time at the system decays to half the S1 population and iii) as an average value of decay time.The predicted 281 fs (from the fitting), 253 fs (from half of the S1 population), and 265 fs as the average decay time values must be compared with the observed 260 fs value. 2 The S1 vibrational frequencies (property 4) of the δop (60 fs and 40 fs periods, equivalent to 565 cm -1 and 847 cm -1 ) and BLA (23 fs period, equivalent to 1450 cm -1 ) are obtained based on their average progressions (Fig. S2d).These are defined as the numerical average of the corresponding δop and BLA values at each time point during the excited state progression.There is no experimental value for δop, but the BLA frequency value compares with the observed values of 21 fs, equivalent to 1572 cm -1 .The Φcis-trans (property 5) was calculated as the ratio of the number of trajectories forming the photoproduct (i.e. this is determined by looking at the α value at the last time step) over the total number of decayed trajectories.The predicted and observed values are 0.30 and 0.21, respectively.In conclusion, the values of the "observables" 1-5 predicted based on the MeO-NAIP@MeOH QM/MM model and population dynamics indicate a semi-quantitative agreement with the experimental observations.These properties have been computed, limiting the simulation (mainly due to the high computational cost) to 200 trajectories.

Section IV. Statistical analysis
An important part of the present study is the statistical analysis of the rPSB11@Rh and MeO-NAIP@MeOH hop points.Accordingly, the following properties have been determined at each A dτ/dt decay < 0 is not a sufficient condition for reactivity.As discussed in the main text, the populations of reactive trajectories for the rPSB11@Rh and MeO-NAIP@MeOH systems are directly associated with dτ/dt decay < 0, with a 15% tolerance for the validity of this relationship.
Similarly, we can establish the relationship between unreactive trajectories and dτ/dt decay > 0. This relationship is supported by the relatively large percentages (81% and 92% for the natural and synthetic motors, respectively) of trajectories with dτ/dt decay > 0 that are indeed unreactive in solvated conditions.However, as we discussed in the main text, these relationships are not equally valid for the artificial system.In other words, most of the reactive trajectories have dτ/dt decay < 0, but not all the population fractions with dτ/dt decay < 0 react, as shown in Table S2.Specifically, only 52% of the trajectories with dτ/dt decay < 0 are reactive, and therefore not all the unreactive trajectories have dτ/dt decay > 0. 1. % with respect to the full ddt decay > 0 or ddt decay < 0 population.2. reactivity criterium defined looking at the S0 configuration reached after the hop.
Section V. A promoter modulates the dτ/dt amplitude.
We construct a basic model of the average progression of the populations by assuming that α has two components, αI and αII, associated with a monotonic progression towards ISS1/S0 and with the δop-coupled oscillatory motion, respectively (see Fig. S3a, top-left).
Consistently with trajectory visualizations, αII -0.5δop describes a periodic out-of-phase change in pyramidalization, namely a change from sp 2 to sp 3 hybridization and back, at C2 and C3 (see Fig. S3a, top-right) that can also be described as an R1, R4 wag coupled with a C1, C4 wag.In our approximate model of the average progression, αI represents the isomerization mode, and dαI/dt is considered constant, while dαII/dt and dδop/dt are harmonic functions characterized by phase, period, and amplitude.The dαI/dt value and the dαII/dt parameters for rPSB11@Rh and MeO-NAIP@MeOH are obtained by fitting the average dα/dt value in Fig. S3b   According to our model, the average overlap velocity is dτ/dt = dαI/dt + d(αII -0.5δop)/dt.This expression points to two effects impacting the population fraction with dτ/dt decay < 0. The first operates in systems with a short IDT and narrow DTL (e.g.rPSB11@Rh) where the isomerization velocity dαI/dt allows the center of a compact population to enter the ISS1/S0 and decay on a timescale of half αII -0.5δop period.In these systems, the phase of d(αII-0.5δop)/dt(i.e. the direction of the pyramidalization velocity) at decay determines the dτ/dt decay < 0 fraction.This is illustrated in Fig. S4a, where two compact sets of trajectories reach the decay region at different times.If at decay, d(αII -0.5δop)/dt is negative (i.e.αII -0.5δop is decreasing), then dτ/dt decay < 0. In other words, during a fast CCW isomerization where dαI/dt < 0, the dτ/dt decay < 0 fraction is maximized when d(αII -0.5δop)/dt < 0 and minimized when d(αII -0.5δop)/dt > 0 at the point of decay.Thus, the pyramidalization velocity promotes the power-stroke that, when synchronized with dαI/dt, will periodically enhance the absolute amplitude of dτ/dt decay < 0. We call αII -0.5δop the power-stroke promoter or, simply, promoter.
The second effect occurs in systems with long IDT and, therefore, large DTL corresponding to a broad S1 decay and wide distribution of low amplitude dαI/dt < 0 values at decay (e.g. as in MeO-NAIP@MeOH).The decay of such a diffuse population would span several αII -0.5δop oscillations (Fig. S4b), leading to a decay pattern displaying multiple alternate positive and negative d(αII -0.5δop)/dt fractions thus leading to a total dτ/dt decay < 0 fraction approaching 50%.The red circles represent reactive decay events while the blue circles represent unreactive events.Bottom, corresponding time progression of the α II -0.5op mode.The diagram shows that the two fast populations decay in correspondence of different phases of α II -0.5op.The negative phase corresponding to the fastest population leads to large (left) dτ/dt decay < 0 fraction while the slightly slower population leads to a decreased dτ/dt decay < 0 fraction (actually a large dτ/dt decay > 0 fraction).b) Same as previous panel but for a population decaying slowly.The corresponding wide distribution of αI velocities leads to a population decay through multiple αII -0.5op phase variations leading to multiple enhancement and decrease of the produce dτ/dt decay < 0 population fraction.c) Same as previous panel but for an oscillatory component resulting from the superposition of two modes called i and ii (see dashed curves): one high frequency (similar to the oscillatory component in panels a) and b) but lower amplitude mode and one low frequency but higher amplitude (e.g. resulting from an S1 ring-inversion motion ρ) respectively.A wide distribution of αI velocities leads to a population decay recovering the characteristics seen in panel a where the population can be divided in fractions decaying with different phases of the coupled oscillatory motion.Again, the fraction decaying with a negative oscillation phase leads to a dτ/dt decay < 0 and therefore to reactive decays.
In the main text, we use the results of the above model to discuss the mechanism of Φ iso modulation.However, for convenience, there we assume, both for each trajectory and for the population (average) values, a proportionality between the directly computable dα/dt and dαI/dt (i.e.we retain only its monotonic, not oscillatory character) and between -0.5dδop/dt and d(αII -0.5δop)/dt (i.e.ignoring the α oscillatory character).

Model details.
In our approximate model of the average progression, αI represents the isomerization mode, and dαI/dt is considered constant, while dαII/dt and dδop/dt are harmonic functions (2) characterized by phase (b), period (T), amplitude (A), and vertical shift (c).
The dαI/dt parameters are determined by approximating the αI curve to a straight line, justified by the quasi-linear monotonic progression towards ISS1/S0 that it describes in both systems.Therefore,  S3 shows all the model's parameters.Section VI.Impact of the (catalytic) molecular environment.
Based on Fig. S6 (and Fig. 5 d and e, main text), it is evident that the pyrroline ring oscillates between upward and downward inversions in isolated conditions.In contrast, the same ring adopts a planar configuration in solution, and the ring-inversion is much slower.One hypothesis is that this behavior is dependent on the distinct electronic structures of the ring in the two environments.
In the presence of a polar solvent, the S1 electronic structure of the pyrroline ring stiffens the ring, significantly increasing the ring-inversion barrier and limiting its oscillations.However, this stiffening effect does not occur in isolated conditions, and the ring becomes flexible, oscillating between half-chair-type conformations (out-of-plane).The molecule's electronic structure and corresponding bond lengths appear to explain why the pyrroline ring is rigid in one environment but not in another.

S18
The variation in the amount of positive charge of the pyrroline moiety along some random trajectories was followed in both environments (see Fig. S7).The corresponding charge plots on S1 reveal distinct behaviors of the isolated (orange) and solution (black) environments, which support the mechanistic hypothesis discussed above and the possible impact on the isomerization quantum efficiency.Firstly, at the beginning (0 fs) of the dynamics, the S1 positive charge of the solvated system is found to reside almost entirely on the pyrroline moiety, as expected for a system with a counterion (this is a virtual counterion formed by the oriented dipoles associated to the solvent methanol molecules) that keeps the charge close to the N atom.In contrast, the isolated system shows a more distributed charge on S1 (~0.5 on the pyrroline moiety), corresponding to a delocalized electronic structure connected with the absence of a counterion.Secondly, the lowfrequency oscillation observed in the pyrroline moiety charge during the S1 dynamics appears to be linked to a periodic ring-inversion motion.Notably, the pyrroline moiety charge evolution appears to complete one full oscillation for the solvated system (black) and two oscillations (i.e. corresponding to a ca.halved period) for the isolated system, possibly reflecting the level of stiffness imposed by the electronic configuration over the ring-inversion motion.In this sense a larger frequency would indicate the presence of a stiffer approximately planar ring (see also below).C. CASSCF energy profile for these random trajectories.
To better understand how the electronic structure affects the mechanical (i.e. the low-frequency vibrations such as the ring-inversion) behavior of the pyrroline ring, we have modeled and studied two S0 model systems that "mimic" different charge distributions on the pyrroline moiety (see Figure 5h, main text).More specifically, such model systems are assumed to represent the different types of electronic configurations observed in isolated and solvated conditions during the S1 dynamics of MeO-NAIP and, because of that, help to computationally determine whether the dynamic and shape of the potential energy surface associated with a specific electronic structure is consistent with the S1 dynamics observed for MeO-NAIP.The two selected model systems are: i. a neutral enamine, that mimics a pyrroline moiety featuring a sp 3 N atom and a localized double bond in position C3=C4 hypothesized to be the dominant electronic structure of a solvated MeO-NAIP in the S1 state.Consistently with the plot in Fig. 5g bottom, in the main text, such an electronic structure is the one generated via the large charge-transfer motion occurring upon S1 relaxation in the solvated rotor.
ii. a cyanine, mimics a partially positive charged pyrroline moiety featuring highly delocalized N=C2 and C3=C4 double bonds consistently with the charge plot in Fig. 5g top, main text, and the ring-puckering progression for an isolated MeO-NAIP in the S1 state in Fig. S8.
The S0 structures of the models were optimized at the MP2 level and then subjected to 200 fs dynamics at the Hartree-Fock level to extract the final momenta and positions.These were used as starting points for 500 fs S0 classical trajectory computed at the CASSCF level (in all cases the 6-31G* basis was employed) in isolated conditions.The active space comprises 6 electrons in 5 πorbitals, To gain a better understanding of the relationship between ring-inversion and electronic structure, we have investigated the shape of the S0 potential energy surface along the out-of-plane ring distortion.This required the identification of two minima corresponding to inverted ring conformations (half-chair and inverted half-chair) and the transition state (TS) connecting them, which defines the energy barrier that must be overcome for the ring-inversion.The hypothesis is that such energy barrier, if it exists, may restrain the pyrroline moiety oscillatory motion which would instead require, to promptly oscillate, a single potential energy wall with a suitable curvature.
Table S4 summarizes the results of the energy profile mapping along the ring-inversion coordinate that started by determining the conformational minima involved in the ring-inversion and their transition states (TS).To identify the TS structure, we initiated a search for the saddle point in the S0 PES and a subsequent optimization of the structure found.We then conducted a verification step to confirm that the TS describes the reaction in question, which included hessian calculation to find the imaginary frequency and the corresponding reaction vector connecting the two conformational minima.All optimizations were performed at the 3-root-CASSCF level in the gasphase for consistency with the MeO-NAIP studies.
Table S4.Relative CASSCF energy (with respect to the lowest minimum) and ring-inversion angle for the conformational minima and TS structures of the three model systems studied.Table S4 shows that the only model with well-defined conformational minima is the enamine model.These minima are not planar and are separated by a ring-inversion energy barrier of about 4 kcal mol -1 (as schematically shown in Fig. S8b and Fig. S9).In fact, the located minima correspond to mirror images displaying a pyramidalized (sp 3 ) nitrogen with an inverted configuration in the pyrroline moiety.The TS connecting these minima is, therefore, planar.In contrast, the cyanine model has nearly planar conformational minima, which means this model displays, substantially, a single conformer located at the center of a relatively shallow potential wall (see Fig. S8b).These models are two cases with the charge translocated (enamine) and with the charge strongly delocalized (cyanine).In the cyanine, where the N atom is sp2, the planar ring must find itself at the center of shallow energy profiles along the ring-inversion motion, allowing the system to oscillate around a planar configuration.While in the enamine (sp 3 hybridization), the system has, hypothetically, a lesser propensity to planarize the pyrroline moiety leading to a higher oscillatory frequency around a very distorted ring value.The simulation indicates the existence of a different potential energy valley for each model, as indicated in Fig. S8b.
The frequency of the ring-inversion mode was determined by computing the Hessian at the minimum geometry for each model.The resulting frequencies were 174 cm -1 (enamine), and 80 cm -1 (cyanine).These frequencies agree with the observed dynamics for the models (see Fig. S8b).
The enamine model completed three oscillations at a higher frequency with limited amplitude due to a 4 kcal mol -1 barrier, while the cyanine model completed one full oscillation at lower frequency.A further test was carried out to see if the Φ iso inhibitory effect observed for MeO-NAIP in methanol is exclusively due to electronic reasons (as concluded above) or if additional effects (e.g., hydrogen bonding, steric hindrance, or others) brought up by a different environment is modulating the promoter motion.Accordingly, we constructed a model of MeO-NAIP in the aprotic polar solvent dimethyl sulfoxide (DMSO) following the same protocol already described for methanol solvent to evaluate the ring-puckering ρ mechanism in a different environment and extract some valuable conclusions.
We evaluated the ρ evolution along the S1 population dynamic (500 fs) represented by 100 trajectories of the resulting MeO-NAIP@DMSO model and compared it with the population dynamics reported for isolated MeO-NAIP and MeO-NAIP@MeOH (see Figure S10).The results show that both polar solvents quench the ring-puckering motion with respect to isolated conditions.
However, the population fraction that overpasses the planarity energy barrier and produces a ring oscillation between positive and negative ρ values is slightly higher in DMSO (34%) than in MeOH (26%).Notice that the population fraction is selected based on trajectories that complete one oscillation within the initial ca.250 fs which also coincides with the S1 lifetime (at least in isolated condition and MeOH).As discussed above, this quenched behavior in MeOH correlates with a reduction in quantum yield (Φ iso ), as it limits the fraction of the population capable of achieving significant ring distortion necessary to enhance the magnitude of dτ/dt velocity.The Φ iso evaluation in DMSO is not discussed in the present study since this environment dramatically changes the excited state lifetime (beyond 500 fs) due to an interaction between bounded (S2) and unbounded (S1) electronic states limiting the number of MeO-NAIP@DMSO trajectories that decay to S0.The investigation of the DMSO must be continued but due to the high computational cost could not be completed within the scope of the present study.Although we cannot correlate the higher percentage of the fraction conducting to oscillation with Φ iso in DMSO, our MeO-NAIP@DMSO simulation demonstrates the potential for ring-inversion in each environment with very different features (volume and viscosity).The analysis presented above is further validated by charge distribution studies of the pyrroline moiety on the S1 state (see Figure S11).This confirms the dominant influence of electronic factors in governing the ring-puckering phenomena quenched in polar solvents.Collectively, our findings elucidate the complex interaction between molecular geometry, solvent interactions, and electronic structure, all of which are instrumental in shaping the photophysical properties of biomimetic rotors like MeO-NAIP.
Section VII.Coupling of the ρ promoter mode with β and δop.
In our previous discussion, we uncovered a distinct, slower promoter mode ρ, which operates on a timescale of approximately 250 fs.This is in stark contrast to the well-documented 40 fs hydrogen out-of-plane wag mode, δop, observed in rPSB11@Rh and also present in the synthetic rotor MeO-NAIP.It's crucial to emphasize that this newly identified ρ mode isn't merely another manifestation of previously reported wag modes.Instead, it represents a slower ring-inversion motion that perfectly synchronizes with the reaction coordinate, resulting in a substantial increase in quantum efficiency.This mechanism goes beyond previous explanations found in synthetic rotor literature and carries direct implications for rotor engineering.
To further illustrate the distinction between the ring-puckering motion, ρ, and the COOP motion, δop (analogous to the previously reported HOOP motion in rPSB11@Rh), we refer to Figure S12.
This figure provides a clear visualization of the markedly different frequencies characterizing these two modes.Specifically, ρ (orange curve) exhibits a larger oscillation period of approximately 250 fs, whereas δop (blue), which is directly related to β (black), displays a much shorter period of approximately 40 fs.Notably, the promoter ρ is intricately coupled with the motion describing the substituent wag relative to the molecule's conjugated framework β.This coupling leads to periodic changes in the amplitude of the β oscillation, occurring roughly every 200-250 fs.Consequently, these amplitude variations in β have a direct impact on the amplitude of δop, τ, and subsequently result in enhanced quantum efficiency, Φiso.
To offer visual support for the concepts discussed above, we have included accompanying movies that depict the distinct nature of these vibration modes in MeO-NAIP@gas: 1) the local 40 fs period mode β, and 2) the approximately 250 fs period ring-inversion mode ρ.See Supplementary Movie 1 and 2 for β and ρ respectively.Supplementary Movie 3 shows the synchronization of these quantities.

Figure S2 .
Figure S2.Population dynamics analysis.a) The absorption band is computed to determine λmax value by Gaussian fit of the total population: solution (black curve) and isolated conditions (orange curve).b) Photoproduct (NAIP e-isomer) formation from sub-150 fs fastest decay trajectory.The curves indicate the excitation energy progression, and the dashed red line indicates the S0-S1 excitation energy for the fully relaxed NAIP e-isomer structure.c) Excited state lifetime fitting.The S1 population decay curve in solution (black) and isolated (orange) conditions, with theirs corresponding fitting function (red).d) Average value progression of δop (in blue) and BLA (in brown) for the S1 population.FFT analysis is used to determine the frequencies.

Scheme 1 .
Scheme 1. Analysis of the hop points of the entire population.The left and right branches correspond to analysis carried out according to reactivity (left) or geometrical (right) criteria.In the left part of the diagram, the reactive subpopulation (red box) is analyzed to find out, for instance, if all trajectories in the subpopulation have dτ/dt decay < 0.
top.The -0.5dδop/dt S11 parameters are instead obtained by fitting the average values of Fig. S3b bottom.The results of the fitting are graphically displayed in Fig. S3c.

Figure S3 .
Figure S3.Analysis of the average α and δop progressions.a) Left.Schematic representation of the linear (αI) and a harmonic (αII) component of α skeletal twist (or wag).Right.Model expression of τ expressed in terms of α components and schematic representation of its total oscillatory component.b) Top, progression

Figure S4 .
Figure S4.Progression of the monotonic (quasi-linear) and oscillatory component of τ.A replica of Figure 6 from the main text with reordered panels to better explain the basic model.a) Top, schematic representation of the αI progression and decay associated with two fast-reacting populations (represented by Gaussian profiles).The dark gray area corresponds to the intersection space or decay region (ISS1/S0).
Fig.S3b top).The -0.5dδop/dt parameters are instead obtained by fitting the average values (yellow curve in Fig.S3b bottom).The resulting dαI/dt, dαII/dt, and -0.5dδop/dt models are graphically displayed in Fig.S5a, and once applied d(αI + αII -0.5δop)/dt, the resulting curve corresponds to dτ/dt.The result of such calculation is displayed in Fig.S5btop and can be compared with the

Figure S5 .
Figure S5.Analysis of the average of dτ/dt progressions.a) Modelled velocities of the oscillatory τ component dαII/dt and -0.5dδop/dt.b) Top, resulting dτ/dt model.Bottom, progression of dτ/dt for rPSB11@Rh (left) and MeO-NAIP@MeOH (right).The black lines represent the population motion along S1 before the decay point (represented by red and blue circles).The yellow curves follow the average value.The horizontal dashed line corresponds to the constant dαI/dt value.

Figure S6 .
Figure S6.Comparison of the ring-inversion evolution along dynamics of the isolated and solvated MeO-NAIP chromophore.The decay points for reactive and unreactive trajectories are marked with red and blue circles respectively.a) ρ evolution (dihedral).b) dρ/dt evolution (dihedral velocity).

Figure S7 .
Figure S7.Charge distribution and energy profile of MeO-NAIP.a) MeO-NAIP structure is divided into two moieties: indanylidene and pyrroline.b) Distribution of the positive charge of the pyrroline moiety

Figure S8 .
Figure S8.Study of the model systems.a) Time progression of dρ/dt (i.e.pyrroline moiety ring-puckering of MeO-NAIP.b) Comparison between the average time progression of the ring-inversion angle (ρ) (yellow curve inverted from Fig. S8a to match the CW rotation of the models) observed during the S1 dynamics of MeO-NAIP isolated and the S0 dynamics of two models: enamine (black) and cyanine (orange).

Figure S9 .
Figure S9.Enamine model TS and minima structures involved in the ring-inversion process.The optimized TS structure corresponds to a planar configuration of the ring and the reaction vector extracted from this calculation allowed to verify that the TS structure is the one connecting the two minima (reactant and product) with two half-chair configurations up and down of the ring.The ring-inversion energy barrier was determined at 4 kcal mol -1 over the minima.

Figure S10 .
Figure S10.Evolution of the ρ angle across various environments.The top panel illustrates the full population dynamics, while the bottom panel highlights the percentage of sub-population fraction.achieving a complete oscillation within the initial ca.250 fs coincides with the S1 lifetime and the intrinsic period of ρ.Black trajectories denote the population motion, and the yellow curves follow the average value.

Figure S11 .
Figure S11.Time progression of the average S1 charge on the pyrrolinium moiety of MeO-NAIP in three different environments and along the same trajectory set of (left) Figure S10, top panels, and (right) Figure S10, bottom panels.

Table S1 .
Comparison between the observed experimental parameters and the computational ones.

Table S2 .
Analysis of the population reactivity.The percentages correspond to rPSB11@Rh and MeO-NAIP@MeOH population fractions satisfying the criteria given on the left entry.The values in square brackets refer to the isolated chromophores.

Table S3 .
Harmonic model parameters are obtained by fitting the computed average values of dα/dt and -0.5dδop/dt, while dαI/dt is assumed to be constant and extracted from the slope of a linear equation.